STUDYING RADIOCARBON PAPERS MAY SOLVE THE ENIGMA OF THE RADIOCARBON DATING OF THE SHROUD OF TURIN.

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1 STUDYING RADIOCARBON PAPERS MAY SOLVE THE ENIGMA OF THE RADIOCARBON DATING OF THE SHROUD OF TURIN. Remi Van Haelst Note: Most data used in this paper are taken from peer reviewed papers, published by radiocarbon experts. I strongly advice all those interested in a scientific examination of the radiocarbon dating of the Shroud to do the same. In Volume 337 N 6208 of the Nature magazine of 16th February 1989, the results of the radiocarbon dating of the Shroud of Turin were published. The independently obtained results from the laboratories of Oxford, Zurich and Tucson, all using AMS, were statistically evaluated by the British Museum. The conclusion was that the linen of the Shroud of Turin is mediaeval, with at least 95% confidence. In theory there are FOUR types of distributions. (1) Distribution Symbol Type Symbolic form. Normal Z Individual observations. Z = (x ù)/ Student t Sample means t = (X ù)/(s/n 0.5 ) Chi² Chi² Sample variances Chi² = s²/( ²/d.f) ANOVA F Ratio of TWO sample F = S 1 ² / S 2 ² (= Inverted Beta) variances The statistical analysis, conduced by the British Museum, was made on the basis of a Chi² distribution, in an adapted version by Ward and Wilson. Strangely, on page 613 one reads that Dr. Leese used ANOVA: The value of d, which lies between the inter- and intra laboratory degrees of freedom was estimated at 5, on the basis of an analysis of variance (ANOVA) on the 12 individual measurements supplied by the laboratories. (2) In theory, ANOVA is more robust than Chi², certainly when analysing radiocarbon data, obtained by AMS. The reason for this is that in AMS, each date is the mean of a number of runs, in which are measured a number of targets (or replicates).

2 In ANOVA, one compares the variability between laboratories with the variability within each laboratory. The use of ANOVA is approved by NIST. (3) Example: Under Table 1 (2) one reads the following remark: One anomalous replicate (of 6) obtained for sample for independent measurement O2.2b; if rejected it reduces date by 40 years, final date quoted actually reduced by 20 years. Being a graduate chemist, trained to judge industrial laboratory results in the PPM range, I immediately spotted some discrepancies between the 12 individual data in Table 1 and the 3 means given in Table 2. In reality the Chi² value given as 6.4 is 8.5, a value much greater than the maximal test value 5.99, for the claimed 95 % confidence. Such a large Chi² value excludes a 95 % confidence. Nature Table 2 versus computer recalculations. Ar Ox Zu W. Mean Chi²: 6.4 % SL: 5 Ar Ox Zu W. Mean Chi² 8.6 % SL:1.4 Computer calculations, based on personal correspondence with Ward & Wilson. Approved to be correct by Dr. Morven Leese of the British Museum. Also suspicious are the different values for - C for samples cut from the same small piece of linen. In Nature Table 1 is noted Arizona: - 25 Oxford: -27 Zurich: o/oo Note 1 o/oo 13 C is many times the whole content in 14 C. In time several statisticians came to the same conclusion: The Nature data are not supported by statistical analysis. Applying Bayes statistics, Andrés Christen used the radiocarbon data for the Shroud as an example. (4) He concluded: The dates 795 and 591 are most probably outliers. In New York (1997), Dr. Marion Scott (Glasgow), a member of the panel on radiocarbon, refused to perform her own EEM ~ EEM calculations, using the Nature data for the Shroud. (5)

3 ****** Finally some of the radiocarbon scientists involved agreed with my justified criticism, by correctly assuming that the errors were not large enough to explain an error as large as 1300 years. But none of them did reply to the simple question: HOW DID ONE OBTAIN THE CLAIMED 95 % CONFIDENCE? Because none of the peers did make any remark, the editors of Nature simply refused to comment on my criticism. Strangely, the same goes for the authorities in Turin. When meeting Prof. Gonella in Paris (1989), I asked him why he did not spot the wrong Arizona error in Table 2. He never spoke to me again. After some extended correspondence with Prof. Hedges & Dr. Ramsey (Oxford) and Prof. Jull (Tucson) the matter was solved on the basis of a paper by Burr et al. (5) Here is explained how the AMS facility of Tucson is continuously monitored to keep the deviation of the AMS machine within the limit of 0.3 % Random Machine Error (RME). For RME values > 0.3, the unit is stopped for tuning up and eventually repairs. Between March and August 2005, the Arizona facility was stopped FIVE times, because of RME Values > 0.3 %. To test the AMS facility, in BLIND, series of 8 standard samples are measured 6 times, under the same conditions. To show the power of ANOVA, I asked Prof. Jull, to give me access to these data. Studying the Burr paper, I was surprised to learn how variable AMS measurements are and how easily samples can be contaminated. The 14 C counts vary between ~ 24000, while the ratio 14 C/ 13 C vary between 16 ~ 24. Note that the normal ratio is 1.1 x Using statistical analysis and error reduction (7 & 8) the 48 data in Table 2a, one obtains a number of coefficients ranging from till In theory, a positive ANOVA analysis should result in an F value BELOW the F value for 6 x 8 measurements at 95 % confidence. These data, in function of the inter- and intra- degrees of freedom are given in statistical tables. At 95% confidence, for 8 runs with each 6 measurements, with a degree of freedom {inter (8 1) and intra (48 8)} the MAXIMUM F value is 2.73.

4 ***** The ANOVA analysis of the measurements of the 48 standard samples, as given by Burr resulted in a POSITIVE F value of 1.3 < Prof. Jull was very pleased with the result and agreed that ANOVA could be a useful tool in analysing radiocarbon data. Then I analysed the following set of 48 data Sum Total = Total squared sums: 52150² ² ² ² ² ² ²= Total of 48 squared data: 8630² ² ² ²= Determination of the coefficients Number of runs = 8 Number of targets pro run = 6 Total of data = 48 Factor A = ²/48 = Factor B = /6 = Factor C = = ANOVA DF Between = = / 7 = Residue = = / 40 = 5465 Total = = F = 40543/5465 = 7.4 Note: The RESIDUE should be equal to the total VARIANCE for the 8 runs. Conclusion: The ANOVA test 7.4 >> 2.73 is NEGATIVE. Note: Today, there are several websites, giving direct ANOVA results. One only needs to enter for each run: the number of targets, the means and standard deviation. In no time, the computer gives the F value and the Probability level. Because % 14 C data are log-normally distributed, small errors are possible.

5 To my surprise, Prof Jull asked me where I got this information, for normally no laboratory will give this kind of information. Then I told Jull that I used the EIGHT original Shroud data, obtained by Arizona, multiplied by the 48 coefficients, given by Burr in table 2b. As a professor, Jull replied: I have to give you marks for perseverance. The data used by you are correct. To day we should perform much better. Alas, Burr did not answer my questions. ****** Studying a paper by Hodgins, Butters, Ramsay and Hedges (9) I learned that contamination of dead wood as old as years, by acid and enzyme hydrolysis may cause significant enrichment in 14 C. Acid treatment: One obtained 42 µg of pure carbon, containing % 14C. Enzyme treatment: A: One obtained 15 µg of pure carbon, containing % 14C B: One obtained 320 µg of pure carbon, containing % 14C. Note: This paper shows clearly, that sample contamination by modern carbon is not excluded. The same phenomenon was already noted by Lloyd Currie, writing in NIST. He also analysed the Nature data, explaining the variability of the data for the Shroud, by the irregularity of 14 C concentration, due to atmospheric disturbances. (10) Analyzing NIST dust samples SRM 1649a, different rates in 14 C in char and soot were found. In material from the Dent Mammoth one found 14 C values between 2500 and 4000 counts. He announced near future 14 C measurements, based on a real isotopic mass balance. Acknowledgments: I like to thank: Bryan Walsh, for his precious technical support. Prof. Jull and Dr. Ramsey, for providing me valuable information. *****

6 References. 1. Perry s Chemical Engineers Handbook 2. Damon et al Radiocarbon dating of the Shroud of Turin (Nature. Volume 327 N pp ) 3. NIST Technical Note B. Taylor & C. Kuyatt. (1994) 4. Andrés Christen. «Summarizing a set of RC Determinations. (Applied Statistics 1994) 5. Marion Scott. Antiquity» Vol. 64 June 1999) 6. Burr et al. «Error Analysis at the NSF Arizona AMS Facilty.» Nuclear Instrument and Methods in Physical Research (Science Direct page 149 ~155). 7. Bevington. Data reduction and Error Analysis for the Physical Sciences. (McGraw Hill Edition 1969) 8. Bevington & Robison. Data reduction (McGraw Hill Edition 1982) 9. Hodgins, Butters, Ramsey and Hedges. The chemical and enzymatic hydrolysis. (Radiocarbon Vol. 47 N 2a. pp ) 10. Lloyd Currie The remarkable Metrological History of RC dating. (NIST Part II. Volume 109 N 2 (2004)

RICHARD BURLEIGH, MORVEN LEESE, and MICHAEL TITS Research Laboratory, The British Museum, London WC 1 B 31)G, England

[RADIOCARBON, VOL 28, No. 2A, 1986, p 571-577] AN INTERCOMPARISON OF SOME AMS AND SMALL GAS COUNTER LABORATORIES RICHARD BURLEIGH, MORVEN LEESE, and MICHAEL TITS Research Laboratory, The British Museum,